Embedded Software for SoC - Grupo de Mecatrônica EESC/USP

On-Chip Stochastic Communication 377
the nondeterministic nature of DSM faults. This suggests that a stochastic
approach (described next) is best suited to deal with such realities.
4. STOCHASTIC COMMUNICATION
The technique we call on-chip stochastic communication implements the NoC
communication using a probabilistic broadcast algorithm [4]. The behavior
of such an algorithm is similar to the spreading of a rumor within a large group
of friends. Assume that, initially, only one person in the group knows the
rumor. Upon learning the rumor, this person (the initiator) passes it to someone
(confidant) chosen at random. At the next round, both the initiator and the
confidant, if there is one, select independently of each other someone else to
pass the rumor to. The process continues in the same fashion; namely,
everyone informed after t rounds passes the rumor at the (t + 1)th round to
someone selected at random independently of all other past and present
selections. Such a scheme is called gossip algorithm and is known to model
the spreading of an epidemic in biology [16].
Let I(t) be the number of people who have become aware of the rumor after
t rounds (I(0) = 1) and let
be the number of rounds until
n people are informed. We want to estimate in order to evaluate how fast
the rumor is spread. A fundamental result states that:
1
with probability 1 [6]. Therefore, after
rounds (n represents the
number of nodes) all the nodes have received the message with high
probability (w.h.p.) [4]. For instance, in Figure 28-2, in less than 20 rounds
as many as 1000 nodes can be reached. Conversely, after t rounds the number
of people that have become aware of the rumor is an exponential function of
t, so this algorithm spreads rumors exponentially fast.
The analogy we make for the case of NoCs is that tiles are the “gossiping
friends” and packets transmitted between them are the “rumors” (see Figure
28-3). Since any friend in the original setup is able to gossip with anyone
else in the group, the above analysis can be applied directly only to the case